A fast image reconstruction method based on Bayesian compressed sensing for the undersampled AFM data with noise

Compressed sensing (CS) can be used to obtain a signal through undersampling and reconstruction, which enables the atomic force microscope (AFM) to spatially under-sample the topography information to increase the imaging rate and reduce the amount of probe-sample interaction. However, the imaging mode of the AFM, which would result in the huge occupation of computing resources including computing time and memory space, makes it inefficient and time-consuming to apply the normal image reconstruction method directly to recover the sample topography from undersampled data. And it is unrealistic to recover a high-solution image by the normal compressed sensing. Here, a novel image reconstruction method based on Bayesian compressing sensing for the undersampled AFM data with noise is proposed to significantly reduce the occupation of computing resources while guaranteeing a high-quality image reconstruction. In the proposed method, the AFM image is regarded as a collection of independent vectors and each vector (a subset of the pixels) is recovered separately. The Bayesian compressed sensing is introduced to provide a better reconstruction performance. The reconstruction experiments demonstrate that the proposed method can significantly reduce the occupation of computing resources while achieving high-quality AFM image reconstruction from the undersampled data with noise. The reconstruction time has been shortened from tens of minutes to less than one minute and the RAM used is reduced to only 1/n(2) of the normal algorithms, which allows the AFM image reconstruction from undersampled data to be easily and conveniently achieved in any personal computer.